1. Find the Big-O of f(n)=log (n+4)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Find the Big-O

8:12 PM Sun 25 Dec
< Ć
●
3.
4.
5.
1.
2.
Solve the following questions:
S
f(n)=2log n and g(n)=n\n
• f(n)=2+1 and g(n)=2"
f(n)=2n and g(n)=3n
f(n)= √logn and g(n)= log log n
то
Find the Big-O of f(n)=log (n+4)
Prove that running time
4
T(n) = n¹ + 20n + 1 is O(n)
T(n) = n¹ + 20n + 1 is O(n³)
4
T(n) = n¹ + 20n + 1 is (n³)
Find the big-O of f(n) = (5n² + 7n -1)(3n³- 4n² +8)
Find the big- of f(n) = 3n+ 10
Find the relation between:
a. n³
b. 10n²
QB
Tutorial No. 1
81%
+:0
• f(n)=2(²n) and g(n)= 2ª
6.
Find the relation between the following functions: f(n) = log n and g(n) = √n. Hint: you may use
L'Hopital's Theorem.
7.
Order the following functions: n, 105, √n, 3", nn.
8.
For function f(n)=log n and time t=1 second, determine the largest size n of a problem that can be
solved in time t, assume that the algorithm to solve the problem takes f(n) microseconds.
9. Suppose you have algorithms with the two running times listed below. Suppose you have a computer
that can perform 6° operations per second, and you need to compute a result in at most an hour of
computation. For each of the algorithms, what is the largest input size n for which you would be able to
get the result within an hour?
Transcribed Image Text:8:12 PM Sun 25 Dec < Ć ● 3. 4. 5. 1. 2. Solve the following questions: S f(n)=2log n and g(n)=n\n • f(n)=2+1 and g(n)=2" f(n)=2n and g(n)=3n f(n)= √logn and g(n)= log log n то Find the Big-O of f(n)=log (n+4) Prove that running time 4 T(n) = n¹ + 20n + 1 is O(n) T(n) = n¹ + 20n + 1 is O(n³) 4 T(n) = n¹ + 20n + 1 is (n³) Find the big-O of f(n) = (5n² + 7n -1)(3n³- 4n² +8) Find the big- of f(n) = 3n+ 10 Find the relation between: a. n³ b. 10n² QB Tutorial No. 1 81% +:0 • f(n)=2(²n) and g(n)= 2ª 6. Find the relation between the following functions: f(n) = log n and g(n) = √n. Hint: you may use L'Hopital's Theorem. 7. Order the following functions: n, 105, √n, 3", nn. 8. For function f(n)=log n and time t=1 second, determine the largest size n of a problem that can be solved in time t, assume that the algorithm to solve the problem takes f(n) microseconds. 9. Suppose you have algorithms with the two running times listed below. Suppose you have a computer that can perform 6° operations per second, and you need to compute a result in at most an hour of computation. For each of the algorithms, what is the largest input size n for which you would be able to get the result within an hour?
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